People have tried many methods to study epidemics. The susceptible, infected, and recovered model (SIR model) is considered as one of the seminal models of epidemics [1]}. A recent work [2]} gives a comprehensive review of the methods to model and analyze Covid-19. Out of these methods, the models relevant to our model are compartmental models. They are prominent methods used for the analysis and prediction of Covid-19 dynamics [2]} [4]} [5]}. However, these works consider only infection from people to people from within the population and do not consider any external source of infection explicitly.
